In this study, we attempted to understand the design of functional materials based on the atomic order crystal structure. Priderite is attractive for one-dimensional super ionic conductors and SYNROC containers for radioactive waste.A solid solution region of priderite was found in the x=1.45-1.80 compositions at about 1200C and the region becomes narrow and converges to ax=1.5 composition with rising temperature. From these results, K-Al-,K-Fe- and K-Mg-priderite with ax=1.5 composition were grown from the melts.Distributions of cations in the tunnel and the relationship between occupancy and super structure were studied by crystal structure analysis. Three kinds of sites were found in the hexahedra located in the tunnels: the center of the tunnel, a site on the bottle neck and a displaced site from the center. Commensurate models of distribution of ions in the tunnel were proposed based on the sites. Six types of models were proposed from the fundamental lattice to a superstructure with six-times the c-axis. Real crystals showed an incommensurate super lattice by X-ray single crystal diffraction. Then, we obtained a result where the incommensurate phase is intergrowth of commensurate phases.